What is the value of $$\text{cot } x$$ when $$\text{sin } x = 0.5$$ and $$\text{cos } x = \frac{\text{\text{sqrt}}{3}}{2}$$ ?

$$\text{cot } x = \frac{\text{cos } x}{\text{sin } x} = \frac{\frac{\text{\text{sqrt}}{3}}{2}}{0.5} = \text{\text{sqrt}}{3}$$

What is the value of $$\text{csc } x$$ when $$\text{sin } x = 0.5$$ ?

$$\text{csc } x = \frac{1}{\text{sin } x} = \frac{1}{0.5} = 2$$

What is the value of $$\text{sec } x$$ when $$\text{cos } x = \frac{1}{2}$$ ?

$$\text{sec } x = \frac{1}{\text{cos } x} = \frac{1}{\frac{1}{2}} = 2$$

Trigonometric Identities and Functions Flashcards: 15 Cards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of cotangent?

Back

$\text{cot } x = \frac{\text{cos } x}{\text{sin } x}$

2.

FLASHCARD QUESTION

Front

What is the definition of cosecant?

Back

$\text{csc } x = \frac{1}{\text{sin } x}$

3.

FLASHCARD QUESTION

Front

What is the Pythagorean identity?

Back

$\text{sin}^2 x + \text{cos}^2 x = 1$

4.

FLASHCARD QUESTION

Front

What is the reciprocal identity for sine?

Back

$\text{sin } x = \frac{1}{\text{csc } x}$

5.

FLASHCARD QUESTION

Front

What is the reciprocal identity for cosine?

Back

$\text{cos } x = \frac{1}{\text{sec } x}$

6.

FLASHCARD QUESTION

Front

What is the reciprocal identity for tangent?

Back

$\text{tan } x = \frac{1}{\text{cot } x}$

7.

FLASHCARD QUESTION

Front

Simplify: $\text{sin}^2 x + \text{cos}^2 x$

Back

1

8.

FLASHCARD QUESTION

Front

What is the quotient identity for tangent?

Back

$\text{tan } x = \frac{\text{sin } x}{\text{cos } x}$

9.

FLASHCARD QUESTION

Front

What is the quotient identity for cotangent?

Back

$\text{cot } x = \frac{1}{\text{tan } x}$

10.

FLASHCARD QUESTION

Front

What is the relationship between secant and cosine?

Back

$\text{sec } x = \frac{1}{\text{cos } x}$

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